# How to analyze the sample means of different treatment conditions

## Description

In a single-factor experiment with three or more treatment levels, how can we compare them to see which one impacts the outcome variable the most?

## Using Matplotlib and Seaborn, in Python

The solution below uses an example dataset about the teeth of 10 guinea pigs at three Vitamin C dosage levels (in mg) with two delivery methods (orange juice vs. ascorbic acid). (See how to quickly load some sample data.)

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from rdatasets import data
df = data('ToothGrowth')

To visually plot the means of the length of the tooth based on the Vitamin C dosage levels we can create a pointplot. We will have to import the `seaborn`

and `matplotlib.pyplot`

packages to be able to create it.

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import seaborn as sns
import matplotlib.pyplot as plt
sns.pointplot( x = 'dose', y = 'len', data = df,
ci = 95, # ci stands for Confidence Interval
capsize = 0.1 ) # the width of the "caps" on error bars
plt.show()

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/tmp/ipykernel_4429/664134235.py:3: FutureWarning:
The `ci` parameter is deprecated. Use `errorbar=('ci', 95)` for the same effect.
sns.pointplot( x = 'dose', y = 'len', data = df,

The point plot informs us that as the dosage levels increase, the tooth length also increases.

To obtain the actual numbers, we can use the `groupby`

function to compute the treatment level means, and the `mean`

function to compute the mean for the entire column.

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df.groupby('dose')['len'].mean()

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dose
0.5 10.605
1.0 19.735
2.0 26.100
Name: len, dtype: float64

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df['len'].mean()

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18.813333333333336

If you wish to display the difference between the overall mean and the group means, you can subtract the overall mean from the treatment level means.

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df.groupby('dose')['len'].mean() - df['len'].mean()

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dose
0.5 -8.208333
1.0 0.921667
2.0 7.286667
Name: len, dtype: float64

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

## Using gplots and emmeans, in R

The solution below uses an example dataset about the teeth of 10 guinea pigs at three Vitamin C dosage levels (in mg) with two delivery methods (orange juice vs. ascorbic acid). (See how to quickly load some sample data.)

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df <- ToothGrowth

To visually plot the means of the length of the tooth based on the Vitamin C dosage levels we can create a pointplot. We will use the `gplots`

package. In the code below, `bars=TRUE`

gives 95% confidence intervals for the means.

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# install.packages("gplots") # If you have not yet installed it
library(gplots)
plotmeans(len~dose, data=df, bars=TRUE)

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Attaching package: ‘gplots’
The following object is masked from ‘package:stats’:
lowess

The point plot informs us that as the dosage levels increase, the tooth length also increases.

To obtain the actual numbers, we can use the code below. The first line converts the numerical dosage values to a categorical variable, which may not be necessary if your data was already categorical.

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df$dose.factor = as.factor(df$dose)
aov1 = aov(len~dose.factor, data=df)
model.tables(aov1, type='means')

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Tables of means
Grand mean
18.81333
dose.factor
dose.factor
0.5 1 2
10.605 19.735 26.100

If you wish to display the difference between the overall mean and the group means, you can simply omit the `type='means'`

parameter.

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model.tables(aov1)

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Tables of effects
dose.factor
dose.factor
0.5 1 2
-8.208 0.922 7.287

To also see the specific values for the confidence intervals plotted earlier, we can use the `emmeans`

package (Estimated Marginal Means or Least-Squares Means).

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# install.packages("emmeans") # If you have not yet installed it
library(emmeans)
emmeans(aov1,'dose.factor')

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dose.factor emmean SE df lower.CL upper.CL
0.5 10.6 0.949 57 8.71 12.5
1 19.7 0.949 57 17.84 21.6
2 26.1 0.949 57 24.20 28.0
Confidence level used: 0.95

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

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